Moment of Inertia of grand action parts.

[Robin Hufford]

John,
     I know you attempt to approximate I here for the keystick and the result
you arrive at here may be adequate for this yet I would suggest a fairly
better measure for the mass moment of inertia for the keystick itself can be
arrived at relatively easily with a little more effort.
     I(g) = 1/12ml^2 is the moment of inertia about an axis perpendicular to
the plane of rotation and passing through the center of gravity of a straight,
symmetric rod which of course of the key, due to flare, particularly,  and
other things is not.  For the moment though, ignoring these complications and
taking the the keystick to be essentially symmetric the formula you suggest is
for determing I can be improved by taking into account the fact that the axis
of rotation of the keystick does not pass through the center of gravity.
     I(g), (correct me here please Don, if I am wrong,) is suitable where the
axis of rotation passes through the center of gravity.  which is not
generally  the case with a piano keystick.   Where such is not the case it is
necessary to use a formulation called the Parallel-Axis Theorem which
basically says that the moment of inertia of an object about an axis different
than one through the center of gravity but parallel to it,  can be calculated
by adding to I(g) = 1/12ml^2 the moment of the distance to the axis along the
body.  The formula becomes(using I(est)) to indicate rotation at the balance
rail, I(est) = 1/12ml^2 + md^2.
     I want to add my thanks to those of others to Don Gilmore for kindly
sharing his expertise with us on these questions
Regards, Robin Hufford

John Hartman wrote:

> Inertia Heads,
>
> The next step toward understanding how the action works when actually
> played is to find the total MOI as measured at the front of the key.
> First we need to find the MOI of the key, wippen and shank. I thought it
> would be useful to find ways to estimate this. The drawing shows a way
> to estimate the MOI of the key. I have ways to estimate the MOI of the
> wip and the hammer/shank as well but first I wanted to se if anyone else
> had ideas on how to do this.
>
> We could use a variety of methods to measure the MOI directly like using
> a torsion table or torsion pendulum. But these are difficult to build
> and calibrate, more useful for demonstrating the principles of inertia
> than for getting accurate measurement. Professional measuring equipment
> is beyond my reach so for now the estimated MOI will have to do.
>
> After finding the MOI of the three parts the total MOI can be figured
> with an equation.
>
> John Hartman RPT
>
> John Hartman Pianos
[link redacted at request of site owner - Jul 25, 2015]
> Rebuilding Steinway and Mason & Hamlin
> Grand Pianos Since 1979
>
> Piano Technicians Journal
> Journal Illustrator/Contributing Editor
[link redacted at request of site owner - Jul 25, 2015]
>
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